Gradient Index Lens for Infrared Imaging

ABSTRACT

A gradient-index lens for directing incident electromagnetic radiation comprises at least one substrate having a plurality of micro-features (e.g., trenches or holes) that may be arranged in a pattern of varied size and/or spacing. Each of the micro-features has at least one dimension that is less than a wavelength of the electromagnetic radiation. The spacing between adjacent micro-features is less than the wavelength of the electromagnetic radiation, and the size and spacing of the micro-features are sufficient to produce an effective refractive index profile of the lens that is graded.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.14/965,863 filed Dec. 10, 2015 which application claims the benefit ofUS provisional patent application 62/106,708 filed on Jan. 22, 2015. Allof these applications are hereby incorporated by reference in theirentirety.

BACKGROUND

The invention relates to optical devices, and in particular to agradient index lens.

Certain existing thermal imaging solutions for night vision are based onuncooled micro-bolometer arrays that are sensitive to long wavelengthinfrared (LWIR) radiation in the wavelength range of about 8 to 15 μm.The infrared (IR) camera typically includes a camera core comprising aFocal Plane Array (FPA), a lens system and an enclosure. The FPAtypically comprises multiple elements—the underlying Read-Out IntegratedCircuit (ROIC), the thermistor or micro-bolometer pixel array which isbuilt on top of the ROIC, usually on the same silicon wafer andintegrated with the ROIC, and a “packaged window” or lid which issubstantially transparent to incoming IR radiation from a source andbonded on top of the FPA with a hermetic vacuum seal. A single lens or asystem of lenses is mounted on top of the FPA.

In certain conventional lenses, an effective index of refraction may bevaried across the area of the lens to focus incident electromagneticradiation. In an example, a convex lens may have a thickness thatdecreases as a function of radial position from its center. In anotherexample, a conventional gradient index (GRIN) lens may have an index ofrefraction that decreases as a function of radial position from itscenter.

Typically, the optical lens system can be complex and involve multiplelens elements. In the case of infrared (IR) imaging optics, the lensmaterial is usually made through diamond point turning of germanium,which can be an expensive process. Traditionally, the approach chosen toenable vacuum has been to use a crystalline germanium lid, and bond itto the FPA package. In order to minimize stresses due to differentialcoefficients of expansion, the FPA wafer is first singulated into dieand mounted on a ceramic package. The germanium lid is then bonded tothe ceramic package under vacuum. In spite of its high cost, germaniumis selected as a lid material because of its low attenuation of infraredlight in the relevant range of wavelengths.

Consequently, many micro-bolometer devices currently available forthermal imaging are bulky, expensive, and largely restricted to specialuse cases such as military or high-end automotive applications. Manyconventional night vision cameras cost several thousands of dollarsapiece, making their integration into mid- and low- range pricedapplications prohibitive. There is a need for a night vision thermalimaging camera core that enables a small form factor and low cost whilemaintaining adequate performance.

SUMMARY

According to an aspect, a gradient-index lens for directing incidentelectromagnetic radiation within a wavelength range of about 8 to 15 μmcomprises at least one germanium or silicon substrate having a pluralityof trenches formed therein. Each of the trenches has at least onedimension that is less than 8μm, and each of the trenches has a ratio oflength to width that is greater than or equal to 3:1. A majority of thetrenches have an aspect ratio of depth to width greater than or equal to30:1, the spacing between adjacent trenches is less than 8 μm, and aneffective refractive index profile of the lens is graded.

According to another aspect, a gradient-index lens for directingincident electromagnetic radiation within a wavelength range of about 8to 15 μtm comprises at least one germanium or silicon substrate having aplurality of trenches or holes formed therein. Each of the trenches orholes has at least one dimension that is less than 8 μm, and the spacingbetween adjacent trenches or holes is less than 8 μm. An effectiverefractive index profile of the lens is graded, and the f-number dividedby the diameter of the lens is less than 1.5/mm.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing aspects and advantages of the present invention willbecome better understood upon reading the following detailed descriptionand upon reference to the drawings where:

FIG. 1 is a schematic, cross-sectional view of a thermal imaging deviceaccording to some embodiments of the invention.

FIG. 2 is a top plan view of a gradient-index lens having concentriccircular trenches, according to some embodiments of the invention.

FIG. 3 is a top plan view of a gradient-index lens having sub-wavelengthdiscontinuities in concentric circular trenches, according to anotherembodiment of the invention.

FIG. 4 is a schematic, plan view of a gradient-index lens havingL-shaped trenches according to another embodiment of the invention.

FIG. 5 is a schematic diagram of a gradient-index lens having trenchesthat are arranged in a pattern of spokes, according to anotherembodiment of the invention.

FIG. 6 is a schematic diagram of a gradient-index lens having trenchesthat are arranged in a pattern of crosses according to anotherembodiment of the invention.

FIG. 7 shows a plot of the effective index of refraction on the leftvertical axis and the corresponding micro-feature size on the rightvertical axis, according to some embodiments of the invention.

FIG. 8 is a chart of a relation between etch depth and trench width,according to some embodiments of the invention.

FIG. 9 is a schematic, side view of a GRIN lens directingelectromagnetic radiation to focused spots on a focal plane, accordingto some embodiments of the invention.

FIG. 10 is a graph showing an example of an effective index profileresulting from a combination of aspheric index coefficients, accordingto some embodiments of the invention.

FIG. 11 is a schematic, side view of two GRIN lenses arranged to directelectromagnetic radiation to focused spots on a focal plane, accordingto some embodiments of the invention.

FIG. 12 is another graph showing an example of an effective indexprofile resulting from a combination of index coefficients, according tosome embodiments of the invention.

FIG. 13 is another graph showing an example of an effective indexprofile resulting from a combination of index coefficients, according tosome embodiments of the invention.

FIG. 14 is another graph showing an example of an effective indexprofile resulting from a combination of index coefficients, according tosome embodiments of the invention.

FIG. 15 is a schematic, side view of three GRIN lenses arranged todirect electromagnetic radiation to focused spots on a focal plane,according to some embodiments of the invention.

FIG. 16 is another graph showing an example of an effective indexprofile resulting from a combination of index coefficients, according tosome embodiments of the invention.

FIG. 17 is another graph showing an example of an effective indexprofile resulting from a combination of index coefficients, according tosome embodiments of the invention.

FIG. 18 is another graph showing an example of an effective indexprofile resulting from a combination of index coefficients, according tosome embodiments of the invention.

FIG. 19 is another graph showing an example of an effective indexprofile resulting from a combination of index coefficients, according tosome embodiments of the invention.

FIG. 20 is another graph showing an example of an effective indexprofile resulting from a combination of index coefficients, according tosome embodiments of the invention.

FIG. 21 is a schematic, cross-sectional view of another thermal imagingdevice according to some embodiments of the invention.

FIG. 22 shows an example of a half-tone mask pattern on a surface of asubstrate, according to some embodiments of the invention.

FIG. 23 is a top plan view of an array of GRIN lenses formed in a lenssubstrate according to some embodiments of the invention.

FIG. 24 is a top plan view of another array of GRIN lenses formed in alens substrate according to some embodiments of the invention.

FIG. 25 shows a schematic block diagram of another thermal imagingdevice according to some embodiments of the invention.

FIG. 26 is a block diagram illustrating the imaging of a scene andreconstruction of the original image according to some embodiments ofthe invention.

FIG. 27 shows a schematic block diagram of another thermal imagingdevice according to some embodiments of the invention.

FIG. 28 is a block diagram illustrating an ideal deep reactive ionetching (DRIE) process.

FIG. 29 is a block diagram illustrating a typical side wall angle in aDRIE process.

FIG. 30 is a block diagram illustrating the stacking of etchedsubstrates to form a GRIN lens according to some embodiments of theinvention.

FIG. 31 is a block diagram illustrating the stacking of etchedsubstrates to form a GRIN lens according to another embodiment of theinvention.

FIG. 32 is a block diagram illustrating a GRIN lens comprising a blindetched substrate with a thin lid, according to some embodiments of theinvention.

FIG. 33 is a block diagram illustrating a GRIN lens comprising athrough-etched substrate with two thin lids according to someembodiments of the invention.

FIG. 34 is a block diagram illustrating a GRIN lens comprising two blindetched substrates bonded to form enclosed trenches or holes according tosome embodiments of the invention.

FIG. 35 shows a schematic, side view of a GRIN lens with diffractiveoptical elements formed in a lens substrate according to someembodiments of the invention.

FIG. 36 shows a schematic, side view of a GRIN lens with micro-featuresformed in two sides of a substrate according to another embodiment ofthe invention.

FIGS. 37A-F are schematic block diagrams illustrating fabrication stepsfor producing a lens with micro-features formed in two sides of asubstrate, according to some embodiments of the invention.

FIG. 38 is a schematic side view of another GRIN lens comprising twosubstrates attached to form enclosed trenches or holes, according tosome embodiments of the invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 1 shows a thermal imaging device 10 that includes a focal planearray (FPA) 22 preferably formed on a wafer or substrate 20. The FPA 22comprises an array of pixels 24 (e.g., a micro-bolometer or other devicethat converts incident electromagnetic radiation to a correspondingelectrical signal). In an example of a focal plane array, the pixels arearranged in rows and columns (e.g., 40×60 pixels to 1,024×768 pixels)with a pitch in the range of about 7 μm to 50 μm. In an example of apixel, each pixel comprises a thermistor that changes its electricalresistance in response to incident electromagnetic radiation (e.g., inthe infrared wavelengths).

The device 10 also includes at least one gradient-index (GRIN) lens 42formed in a lens substrate 40. The lens 42 is arranged to directincident electromagnetic radiation (e.g., infrared rays) to focusedspots on the pixels 24. The lens 42 has an effective refractive indexprofile that is graded (e.g., gradual variations in the refractive indexof the lens). Such variations in the refractive index can be used toproduce lenses with flat surfaces, or lenses that do not have theaberrations typical of traditional spherical lenses. Gradient-indexlenses may have a refraction gradient that it spherical, axial, orradial (e.g., the effective refractive index varies as a function ofradial position from the center of the lens). A spacer or standoffstructure 32 may optionally be used to position the lens 42 at a desiredseparation from the FPA 22 (e.g., the focal length of the lens). In someexamples, the separation of the lens 42 from the pixels 24 provides anoptical path length in the range of 2 to 14 mm. The standoff structure32 may be patterned, for example, from silicon (e.g., by DRIE of a SOIwafer), a metal, ceramic, glass or polymer.

The lens substrate 40 preferably encloses the pixels 24 in a vacuum in aspace between the lens substrate 40 and the FPA substrate 20. The termvacuum is intended to mean a space in which the pressure is lower thanatmospheric pressure. In some embodiments, the standoff structure 32forms the vertical walls around the periphery of the enclosed spacecontaining the pixels 24 between the lens substrate 40 and the FPAsubstrate 20. A hermetic seal may be formed, for example, using a fusionbonding process to bond the FPA substrate 20 and the lens substrate 40to opposite sides of the standoff structure 32. In other embodiments,the lens substrate 40 is attached directly to the FPA substrate 20,e.g., using a fusion bonding process.

The lens substrate 40 preferably has a thickness in the range of 250 to2000 μm to impart bending stiffness and to resist excessive deflection.In some examples, a substrate is a single crystal silicon wafer with adiameter in the range of 100 mm to 450 mm. To aid maintenance of avacuum, a cavity substrate 50 is optionally attached to the FPAsubstrate 20. In some embodiments, the cavity substrate 50 has one ormore cavities 52 fluidicly connected to the vacuum space between thelens substrate 40 and the FPA substrate 20 by means of vias 26 in theFPA substrate 20.

A readout circuit is electrically connected to the pixels 24. In someembodiments, a Read-Out Integrated Circuit (ROIC) underlies the FPA 22.As an example, the readout circuit may comprise an analog-to-digitalconverter, a signal conditioning element, a power conditioning element,a memory element and other elements to translate electromagneticradiation incident on a pixel into a corresponding electrical signal. Insome examples, a ROIC may be implemented using a CMOS process.Preferably, the FPA 22 is built on top of the ROIC on the same siliconwafer or substrate 20 and integrated with the ROIC.

Once the FPA/ROIC substrate 20 has been fabricated, the FPA 22 ispreferably packaged such that it is maintained in a vacuum to minimizeheat transfer between the pixels 24 and the ambient environment throughatmospheric convection. Maintaining a desired level of vacuum (e.g., apressure in the range of 0.1 to 100 mTorr) may optionally be aided byputting getter material 54 in the cavities 52. A getter is a materialthat, when enclosed within a vacuum, helps maintain the vacuum byremoving (e.g., using a chemical reaction or by adsorption) gasparticles that come in contact with it. The getter material maycomprise, for example, an alloy containing zirconium and one or more ofvanadium, cobalt, iron, aluminum, or titanium.

A GRIN lens is an implementation of an optical element that may be usedto focus incident electromagnetic radiation. The macro-scale behavior ofa metamaterial may be understood in terms of the effective medium theory(EMT). Within the context of planar refractive optical elements, EMTstates that the effective refractive index n_(eff) of a heterogeneouselement comprising a two-dimensional array of sub-elements having acharacteristic dimension L and intrinsic refractive indices n₁ and n₂ isgiven approximately by a weighted average of n₁ and n₂ for incidentwavelengths λ satisfying λ>>L (e.g., A>10 L). The exact effectiverefractive index is typically determined numerically through the use ofelectromagnetic simulation software (e.g., OptiFDTD commerciallyavailable from Optiwave), including the effects of polarization andincident plane angle.

In the planar GRIN lens 42, a pattern of micro-features may be variedspatially across the area of the lens to tailor the resulting refractiveproperties of the overall element. The micro-features (e.g., trenches,curved trenches, holes, posts or pillars) can vary in their size,spacing, and placement. Each of the micro-features preferably has atleast one dimension (e.g., width or diameter) that is less than thewavelength of the electromagnetic radiation incident on the lens 42. Theterm “less than the wavelength of the electromagnetic radiation”represents cases in which a size of a dimension (e.g., the width of amicro-feature or the spacing between adjacent micro-features) should besmaller than a wavelength of the electromagnetic radiation incident onthe GRIN lens to ensure effective functioning of the lens in directing(e.g., focusing) the electromagnetic radiation. The wavelengths at whicheach GRIN lens is operated may be different, and therefore the size ofthe dimension that is less than the wavelength of the electromagneticradiation may also be different in different applications of the lens.

The electromagnetic radiation typically has a wavelength in the range of1 to 15 micrometers (μm) for many applications of the lens (e.g., fordirecting infrared rays in the near, mid and far-infrared wavelengthranges). In some LWIR embodiments, the electromagnetic radiation has awavelength in the range of 8 to 15 μm. Each of the micro-featurespreferably has at least one dimension that is in the range of 150 nm to15 82 m and that is less than the wavelength of the electromagneticradiation for the intended operation of the lens. Similarly, the spacingbetween adjacent micro-features is preferably in the range of 150 nm to15 μm and less than the wavelength of the electromagnetic radiation forthe desired application of the lens. In some embodiments, the shortestdimension of each of the micro-features (e.g., its width or diameter)and the spacing between adjacent micro-features are both less than 15more typically less than 8 and in some embodiments less than 2 μm or 1μm. To create optimized lenses, materials with low absorption in thewavelength range of interest are advantageous to mitigate transmissionlosses through the GRIN lens. Materials with suitable properties forinfrared applications include, for example, germanium (Ge), silicon(Si), zinc sulfide (ZnS), zinc selenide (ZnSe), and chalcogenide glass.In some cases Si has the further benefit of enabling lower cost.

In general, the pattern of the micro-features formed in the planar GRINlens 42 may be varied as an arbitrary function of position across thelens element to impart a corresponding profile for the effective indexof refraction. The in-plane pattern of the micro-features in a planarGRIN lens is analogous to the out-of-plane surface profile of atraditional lens in terms of providing a mechanism for tailoring therefractive properties of the resulting lens. In some implementations ofa planar GRIN lens, it may be advantageous to have air or vacuum as oneof the refractive sub-elements. For the purposes of the presentdisclosure, both air and vacuum substantially have an index ofrefraction n=1, and may thus be used interchangeably to describe a“trench” or “hole” type of micro-feature.

In some patterns for implementing the planar GRIN lens 42, the spacingof the trenches or holes may be substantially the same and the width ordiameter of the trenches or holes may be changed across the lenselement. In other examples, both the size and the spacing of thetrenches or holes may be varied. In essence, the ratio of matrixdielectric material to air or vacuum determines the effective refractiveindex of a given unit area. In an example of a planar GRIN lens, asubstrate represents a high refractive index, and a trench or holerepresents a low refractive index. The trenches or holes may be formedusing a variety of manufacturing techniques. In the case of a planarGRIN lens using air or vacuum holes in a silicon wafer matrix, it may beadvantageous to form the holes or trenches using traditionalmicro-electromechanical systems (MEMS) processes such asphotolithographic pattern reproduction, thin film deposition, wetetching and deep reactive ion etching (DRIE).

In other examples, the effective density of a matrix material (e.g., asubstrate) is reduced in a prescribed manner across its area to form theGRIN lens 42. In such cases, the effective refractive index of themedium may again be a weighted average of the matrix material and of airor vacuum, but with the weighting determined by the effective density ofthe matrix material. As an example, a silicon substrate may be modifiedusing a porous silicon process (e.g., a process that substantiallychanges the density of silicon) such as electrochemical etching. Theporous process forms micro-features that are pores in the matrixmaterial to selectively reduce the effective density of the matrixmaterial, and hence refractive index, in a manner that supports focusingor steering incident electromagnetic radiation.

FIG. 2 shows a first example of a GRIN lens 41 having trenches that arecurved (e.g., deviating from straightness in a smooth, continuousfashion). In this example, then lens 41 has a pattern of concentriccircular trenches 66. The trenches 66 are spaced apart with a spacingthat is less than the wavelength of the electromagnetic radiation. Forexample, the spacing is in the range of 150 nm to 15 μm and issub-wavelength. At the center of the lens 41, the trenches 66 arenarrower than toward the edge of the lens where the width of thetrenches 66 increases. At the edge of the lens 41 where more of thesubstrate material is removed, the width of the trenches 66 can increaseand the spacing of the trenches 66 can decrease so that both the widthand spacing are less than the wavelength of the electromagneticradiation (e.g., the width and spacing are both in the range of 150 nmto 15 μm and are both sub-wavelength).

FIG. 3 shows another example of a GRIN lens 43 having curved trenches(e.g., trenches that deviate from straightness in a smooth, continuousfashion). In this example, the curved trenches 67 are shaped like arcs.The arc-shaped trenches 67 are arranged in a pattern of concentriccircles or rings having discontinuities that are less than thewavelength of the electromagnetic radiation. The discontinuities of theconcentric circles or rings are portions of the lens 43 where thesubstrate material remains between the trenches 67 that are formed inthe lens substrate. The discontinuities typically have dimensions in therange of 150 nm to 15 μm and are sub-wavelength in size. Thediscontinuities provide material for mechanical support, especially inthe case where the trenches 67 are etched all the way through the lenssubstrate (e.g., a silicon wafer) and there is no base support material.Many patterns of curved trenches are possible, including trenches whosecross-sectional area is shaped like an arc, spiral, circle or ring. Oneadvantage to curved trenches is that diffraction effects may beminimized.

FIG. 4 shows another example of a GRIN lens 21 having L-shaped trenches69 formed in a substrate. FIG. 5 shows a GRIN lens 23 having trenches 19that are arranged in a pattern of spokes. Radial spokes are shown inthis example, but other patterns are possible including spirals tominimize diffraction effects. FIG. 6 shows a GRIN lens 15 havingtrenches 17 that are arranged in a pattern of crosses.

In general, the trenches may have cross sections that are shaped likearcs, spirals, circles, rings, rectangles, hexagons, L-shaped, spokes,crosses, etc. The cross section of a trench is the intersection of thetrench in three-dimensional space with a plane that is substantiallyperpendicular to a line defining the depth of the trench. Each of thetrenches preferably has a ratio of length to width that is greater thanor equal to 3:1. The ratio of trench length to trench width is typicallyin the range of 3:1 to 100,000:1. The “length” of a trench means thelongest dimension of the cross-sectional area in the plane, and “width”means the shortest dimension of the cross-sectional area. For example,if the trench has a cross-section that is shaped like a rectangle in aplane that is perpendicular to the depth line, then the length of thetrench is the longest dimension of the rectangle, and the width of thetrench is the shortest dimension of the rectangle. In some examples, theratio of the length of the cross-sectional area to the width of thecross-sectional area is greater than or equal to about 50:1, and inother examples the ratio is greater than or equal to 100:1.

The trench width preferably keeps the spacing between the trenches wellbelow the wavelength of the electromagnetic radiation, or unwantedlosses can occur. When forming a trench in a substrate, the rate ofetching varies inversely with trench width, and thus a very narrowtrench will not be as deep as a wider trench. The narrower trenches mayhave a slightly greater density to compensate for the lack of depth.

FIG. 7 shows a plot of the effective index of refraction on the leftvertical axis and the optimal micro-feature size on the right verticalaxis. As the effective index of refraction approaches the index of thebulk material (i.e., very little material removed from the lenssubstrate), the optimal micro-feature size (e.g., width of the trenchand spacing between adjacent trenches) should decrease. Table 1 showsexamples of how to maintain micro-feature sizes well below thewavelength of light in silicon (Bulk index=3.42).

TABLE 1 Effective % Material Trench Trench Index Removed Width (μm)Spacing (μm) 2.21 50% 1 1.0 2.936 20% 0.4 2.0 3.178 10% 0.2 2.0 3.299 5% 0.1 2.0

FIG. 8 shows the impact of decreasing trench width on etch depth; thenarrower the trench the shallower the trench. To create a good GRINlens, the effective index of refraction should be maintained over theentire depth of the GRIN lens. However, given the fundamentalrelationship between etch rate and trench width, the trench width may bemodulated (increased) in some embodiments to account for the shallowerdepth. The relationship between etch depth and the modulated trenchwidth is given approximately by the following equation (1):

Tf=Ti*(Dw/Dn)  (1)

where: Tf=Final Narrow Trench Width;

Ti=Initial Narrow Trench Width; Dw=Wide Trench Depth; and Dn=NarrowTrench Depth.

The width of narrow (shallower) trenches may be increased slightly tocompensate for the shallower trench depth. Of course, the width of thetrenches can be compensated to account for other factors including butnot limited to the change in etch rate due to a high density oftrenches.

In some examples, the present invention provides a design andfabrication method for individual and arrays of batch fabricated GRINlenses that may also serve as part of a wafer-level package (WLP) for aFPA within a camera core. In some examples, a WLP comprises two or moresubstrates that are bonded together (e.g., using a solder, anodic, orfusion bonding process) to enclose an element requiring isolation fromthe ambient environment. For example, a lens may be used to focusincident infrared rays onto an imaging sensor such as amicro-bolometer-based FPA. Batch fabricated arrays of GRIN lenses may beused in configurations that simultaneously support schemes forwafer-level optics (WLO) and WLP. This approach further enablesmulti-spectral, super-resolution, and/or plenoptic imaging schemes.

An imaging lens system produces a focused image at the focal planearray, where the focused spot sizes in the image are ideally about thesize of a pixel. While a near perfect imaging lens system will producediffraction limited spot sizes over the entire focal plane array, it isnot uncommon for an imaging lens system to be much better at the opticalcenter of the lens system and the performance will fall off towards theedges of the focal plane array. The reduction of the performance off ofthe optical center of the lens system can be compensated with imageprocessing techniques like sharpening. An imaging lens system has acharacteristic Field of View related to the specific application of theimaging lens system. Imaging lens system with a narrow Field of View,typically less than 25 degrees are used in applications includingimaging of circuit components on printed circuit boards and electricalwiring. Narrow field of view imaging lens systems are also used insurveillance cameras to provide detailed images of remote scenes.Imaging systems with a medium Field of View, typically between 25 to 60degrees, are used in a range of thermal imaging applications includingsurveillance and security. Imaging systems with a wide Field of View,greater than 60 degrees, are used for automotive and securityapplications.

The production of a lens system that produces a quality image at thefocal plane array may have several characteristics. The lens system mayhave one or more GRIN lens elements with an aspheric profile. Theaspheric profile may differ greatly from a quadratic index profile. Thelens system should have an aperture sized appropriately for the pixelswithin the focal plane array. The lens system should have a Field ofView consistent with the target application. The lens system may haveanti-reflection coatings on the lens surfaces to minimize reflectionsfrom the lens surfaces. The anti-reflection coating can include thinfilm dielectric coating and sub-wavelength structured coatings.

FIG. 9 shows an example of an imaging lens system comprising a singleetched-silicon GRIN lens 71. The lens system targets a narrow Field ofView of 14.5 degrees. The diameter of the lens 71 is chosen to be 5 mmto match the size of a focal plane array 22 with 160×120 pixelmicro-bolometer with 17 μm pixels, and a 3.4 mm diagonal. The lens 71 iscreated by etching micro-features (e.g., trenches or holes having awidth or diameter of 1 μm), 145 μm deep on a 350 μm thick siliconsubstrate. The coefficients of the index profile for the lens system arein Table 2. The index profile of the lens is an aspheric profile.

This surface has the same shape as the Standard surface, with mediawhose index of refraction is describes by

n ² =n ₀ +n _(r2) r ² +n _(r4) r ⁴ +n _(r6) r ⁶ +n _(r8) r ⁸ +n _(r10) r¹⁰ +n _(r12) r ¹²,

where

r ² =x ² +y ²   (2).

TABLE 2 n0  1.1560E+01 nr2 −1.8769E+00 nr4  1.6137E−01 nr6 −2.8632E−02nr8  3.9672E−03 nr10 −2.0614E−04

FIG. 10 shows the resulting effective refractive index profile from thiscombination of aspheric index coefficients. The index profile is at theindex of bulk silicon at the center of the lens (Bulk index=3.42), thusno trenches or holes are etched into the center of the lens. The indexdrops to 1.8 at the edge of the lens. To produce an effective refractiveindex of 1.8, 66% of the material is etched away at the edges of thelens.

Referring again to FIG. 9, the imaging lens 71 produces a set of focusedspots at the focal plane array 22. The strehl ratio of the differentfield points varies from 0.965, nearly a perfectly focused spot, at thecenter to 0.454 at the most extreme field point. The minimum spot sizeis 25 μm, close to the target pixel size of 17 μm. The lens has adiameter of 5 mm. The focal length of the lens is 13.4 mm, and thef-number (f/#) for the lens is 2.68. The f-number divided by thediameter (d) of the lens (f/#/d) is a parameter related to the strengthof the lens. In this example, the f-number divided by the diameter ofthe lens (f/#/d)=2.68/5=0.536.

If we divide the f/# by the diameter of the lens, then we get aparameter that is nominally independent of lens radius. A stronger lensproduces a smaller parameter. The f-number divided by the diameter ofthe lens (f/#/d) is preferably less than or equal to 1.5 (e.g., in therange of 0.05 to 1.5). Table 3 shows examples for lenses havingdiameters in the range of 1 to 5 mm, focal lengths in the range of 1.44to 37.4 mm, and effective refractive indexes in the range from 1.5 (atthe edges of the lens) to 3.4 (at the center of the lens). For smallerlenses, the f/# generally improves (f/#=focal length/diameter).

TABLE 3 Focal Depth of trenches Diameter length f/# f/#/d or holes inlens 5 mm  37.4 mm 7.48 1.496  50 um depth 4 mm  23.9 mm 5.975 1.494  50um depth 3 mm  13.4 mm 4.47 1.489  50 um depth 2 mm  5.95 mm 2.975 1.488 50 um depth 1.5 mm  3.33 mm 2.22 1.480  50 um depth 1 mm  1.44 mm 1.441.440  50 um depth 5 mm 13.39 mm 2.678 0.536 145 um depth

FIG. 11 shows an example of an imaging lens system comprising two GRINlenses 72, 73 etched in silicon. The lens system targets a medium Fieldof View of 35 degrees. The diameter of the lens is chosen to be 3.5 mmto match the size of a 160×120 pixel micro-bolometer with 17 μm pixels,and a 3.4 mm diagonal. The lens system is created by etchingmicro-features (e.g., trenches or holes having a width or diameter of 1μm), 150 μm deep on a 350 μm thick silicon substrate on the first etchedGRIN lens 72 and 150 μm deep on both sides of a second 500 μm thicksubstrate to form the second lens 73.

The lens system uses three GRIN lens surfaces to achieve the steeringfunctions to produce a good image quality over the entire focal planearray 22. The index of refraction profiles of the three GRIN lenssurfaces are shown in FIG. 12. FIG. 13, and FIG. 14, respectively. Thecoefficients of the GRIN lens surfaces are shown in Table 4.

TABLE 4 First GRIN Second GRIN Third GRIN n0  1.1560E+01  8.0000E+00 1.1560E+01 nr2 −2.1875E+00  2.0000E+00 −5.8005E+00 nr4  1.9556E−01−6.2124E−02  1.1448E+00 nr6 −5.8514E−02 −2.0945E−01 −2.7864E−02 nr8 1.9406E−02  2.9043E−02 −1.8085E−02 nr10 −2.4066E−03 −9.9689E−04 2.0056E−03

The strehl ratio of the different field points varies from 0.965, nearlya perfectly focused spot, at the center to 0.71 at the most extremefield point. The minimum spot size is 15 82 m, close to the target pixelsize of 17 μm. The lens system has a 3.5 mm diameter and a 5.5 mm focallength with a resulting working f-number of 1.62. In this example, thef-number divided by the diameter of the lens system(f/#/d)=1.62/3.5=0.463.

FIG. 15 shows an example of an imaging lens system comprising three GRINlenses 74, 75 and 76. The lens system targets a wide Field of View of 80degrees. The diameter of the first lens 74 is chosen to be 2.0 mm andthe interior lenses 75, 76 are 3.8 mm and 4.1 mm in diameter,respectively, to match the size of a 160×120 pixel micro-bolometer with17 μm pixels, and a 3.4 mm diagonal. Micro-features are etched insilicon (e.g., trenches or holes having a width or diameter of 1 μm),150 μm deep on a 350 μm thick silicon wafer for the first lens 74, 150μm deep on both sides of a second 500 μm thick wafer for the second lens75, and 150 μm deep on both sides of a third 500 μm thick wafer for thethird lens 76.

The lens system uses five GRIN lens surfaces to achieve the steeringfunctions to produce a good image quality over the entire focal planearray 22. The index of refraction profiles of the five GRIN lenssurfaces are shown in FIG. 16. FIG. 17, FIG. 18, FIG. 19 and FIG. 20,respectively. The coefficients of the GRIN lens surfaces are shown inTable 5:

TABLE 5 First GRIN Second GRIN Third GRIN Fourth GRIN Fifth GRIN n0 1.1560E+01  1.1560E+01  1.1560E+01  1.1560E+01  1.1560E+01 nr2−2.6482E+00 −1.2326E+00 −1.8858E+00 −3.1849E+00 −3.6213E+00 nr4 3.6805E−01  4.5315E−02  4.5359E−02  2.9811E−01  4.0120E−01 nr6−2.7546E−03 −1.8849E−02 −2.3057E−02  9.1686E−04  6.9815E−03 nr8−7.7755E−03 −1.4555E−03  6.5004E−06 −7.3609E−04 −7.0091E−03 nr10 3.2197E−03 −6.2757E−05  9.0594E−04  1.0071E−04  1.1407E−03

The strehl ratio of the different field points varies from 0.91, nearlya perfectly focused spot at the center, to 0.83 at the most extremefield point. The minimum spot size is 12 μm, below the target pixel sizeof 17 μm. The lens system has a 2.0 mm aperture and a 2.5 mm focallength with a resulting working F-number of 1.27. In this example, thef-number divided by the diameter of the lens system(f/#/d)=1.27/2=0.635.

In the previous examples, wider field of views typically require moreGRIN surfaces to achieve the steering of the electromagnetic radiationto be focused onto the FPA. These specific examples are meant toillustrate the principles of the optical design of various etchedsilicon GRIN lens systems, and are not limiting the to the scope. Manyother values may be selected for the specific depths, trench or holesizes, and index coefficients, as well as different combinations ofparameters and/or materials. Other examples of imaging lens systems arepossible using other lens types in combination with the etched GRINlenses, including but not limited to refractivity etched silicon lenses,diamond turned infrared lenses, a lens formed from a porous Si process,a diffractive optic, a molded glass lens, or a Fresnel optic.

FIG. 21 shows a thermal imaging device 12 having multiple standoffstructures 32, 34 and 36 for holding corresponding GRIN lenses 42, 44and 46. Multiple standoff structures are useful in embodiments thatutilize multiple lenses. In some embodiments, the first GRIN lenssubstrate 40 may effectively take the place of a separate lid wafer aspart of a WLP. Accordingly, the first standoff structure 32 may be usedto form the lateral “walls” of a WLP and to maintain the appropriateseparation (along the optical axis) between the pixels 24 on the FPAsubstrate 20 and the corresponding GRIN lens 42 formed in the first lenssubstrate 40. The height of the first standoff structure 32 may bechosen to correspond to a focal length of the lens 42.

In some embodiments, the first standoff structure 32 is placed andbonded around the FPA substrate 20, and the first lens substrate 40 isplaced and bonded to the resulting assembly at the first standoffstructure 32. In other embodiments, the first standoff structure 32 mayfirst be placed and bonded around the first lens substrate 40, and theFPA substrate 20 is subsequently placed and bonded to the resultingassembly at the first standoff structure 32. The standoffs may be placedusing, for example, a pick and place process. The bonds between the FPAsubstrate 20 and the first standoff structure 32 and between the firststandoff structure 32 and the first lens substrate 40 may be formedusing, for example, a solder, brazing or fusion bonding process. Thestandoffs may be formed using a material such as, for example, a metal,ceramic, glass, polymer, or combinations thereof

In order to minimize heat transfer between the micro-bolometer pixels 24and the ambient environment through convection, a FPA may be packagedunder a vacuum. Thus, the bonds between the FPA substrate 20 and firststandoff structure 32, the first standoff structure 32 and first lenssubstrate 40, and lens 42 should be substantially hermetic. The FPAsubstrate 20, standoff structure 32 and lens substrate 40 may beassembled and bonded (as described above) to form hermetic seals in avacuum environment. Alternatively, the FPA substrate 20, standoffstructure 32 and lens substrate 40 may be assembled and bonded such thata fluidic “port” remains between the packaged volume and ambientenvironment. The package assembly is subsequently evacuated in a vacuumenvironment and the port hermetically sealed.

Some embodiments may further comprise a second GRIN lens 44 arranged todirect electromagnetic radiation to the first lens 42 and disposed at aprescribed distance from the first GRIN lens substrate 40 using a secondstandoff structure 34. The second standoff structure 34 may besubstantially aligned with the first standoff structure 32 such that thesecond lens 44 is substantially aligned with the first lens 42. Thesecond standoff structure 34 may be placed using, for example, a pickand place process. The bonds may be formed using, for example, a solderor fusion bonding process. The second standoff structure 34 may beformed using a material such as, for example, a metal, ceramic, glass,polymer, or combinations thereof. The volume enclosed between the firstlens substrate 40 and a second lens substrate 47 may be open to theambient environment or hermetically sealed and, in the latter case,either maintained at a vacuum or filled with a gas such as air or drynitrogen at a pressure substantially greater than vacuum.

The above concepts are readily scalable to lens systems comprisinggreater than two lens substrates in the optical path by incorporating athird GRIN lens substrate 46 and a third standoff structure 36, a fourthGRIN lens substrate and a fourth series of standoffs, and so forth. Insome embodiments, the standoff structures may be designed to mitigatethe temperature sensitivity of the overall camera core. For example, thematerial of a standoff may be chosen such that the temperaturecoefficient of expansion of the resulting standoff offsets thetemperature coefficient of index of refraction of a lens.

To create the aspheric index profiles of the previous examples, severaltechniques may be employed. In some embodiments, the principles ofhalftoning are be applied to create the varying index profiles. Halftoneis a reprographic technique that simulates continuous tone imagerythrough the use of dots, varying either in size, in shape or in spacing,thus generating a gradient like effect. “Halftone” can also be used torefer specifically to the image that is produced by this process. FIG.22 show an example of the concept of using a “halftone” process togenerate the pattern of trenches or holes in a GRIN lens. The whitecolor represents the unetched silicon and the increasing grey colorrepresents the reduced index of refraction created by the etchedsilicon. The ideal distribution of the index of refraction istransformed by the half-toning process into a series of white and blackpixels, where the white pixels are locations of unetched silicon and theblack pixels are locations of etched silicon. The density of thetrenches or holes increases towards the edge of the lens substrate.

Several mathematical algorithms exist to produce the half-toning processincluding but not limited to Ordered method, Jarvis method, Stuckimethod, Floyd-Steinberg method, and Cardinality-Distribution method. Animportant consideration in the halftoning process is not to produce anyordered areas where the micro-feature sizes approach the wavelength oflight to reduce unwanted diffraction and or scattering effects of theincident light. The halftoning methods of Jarvis, Stucki orFloyd-Steinberg generally produce more uniform distributions of featuresand minimize unwanted diffraction and or scattering effects.

The half-toning process can be further improved by shifting thelocations of the etched micro-features to produce a more uniformdistribution. Unlike traditional halftoning processes used in printing,the location of the trenches or holes in the silicon can be finelytuned. A mathematical method can be applied to the distribution ofetched trenches or holes to minimize spacing when the wavelength of theincident light is approached. The method includes an effective indexcalculation over an area of the etched lens. The effective index isintegrated over a circle or a Gaussian distribution with a diameterequal to the wavelength of incident light. Ideally this effective indexis equal to the desired effective index of the lens design. However, ifthe effective index of the lens differs from the ideal, the position ofthe etched trenches or holes can be modified to bring the effectiveindex closer to the desired value. The method can be applied from thecenter moving out in concentric circles to minimize the differencebetween the ideal and effective index calculation. The method can beapplied iteratively several times to improve the effective indexcalculation.

FIG. 23 shows an example of a 2×2 round planar GRIN lens array 80. Insome embodiments, n×m element arrays or arrays of sub-arrays of planarGRIN lenses may be co-fabricated monolithically on a single-crystalsilicon or silicon-on-insulator (SOI) substrate 81 using traditionalMEMS batch fabrication processes such as photolithographic patternreproduction, thin film deposition, wet etching and DRIE. In thisexample, the array 80 has micro-features 82 that are circular incross-section.

FIG. 24 shows an example of a 2×2 rectangular planar GRIN lens array 83having trenches 87 that are rectangular in cross-section. Each of thetrenches 87 preferably has a ratio of cross-sectional length tocross-sectional width that is greater than or equal to 3:1. In someembodiments, a DRIE process may be used to form a pattern ofsub-wavelength trenches, holes, pores, posts or pillars in a silicon(Si) substrate such that the resulting element imparts a desiredfocusing behavior for incident electromagnetic radiation in accordancewith the EMT. Each planar GRIN lens in an array may be configured toaddress a corresponding FPA on a FPA substrate. In some cases, a FPA maycomprise an array of FPA sub-arrays. Moreover, in these embodiments,each GRIN lens may comprise an array of GRIN “lenslets” configured toaddress corresponding FPA sub-arrays.

In some embodiments, the planar GRIN lens array 83 comprisessubstantially identical planar GRIN lens unit cells. In otherembodiments, an n×m element planar GRIN lens array comprises differentunit cells such as, for example, lenses having different relativeapertures (F/#), anti-reflection (AR) coatings, color filters, opticalaxis orientation, or width or diameter. The differences in opticalbehavior of lens elements within the planar GRIN lens array are impartedby corresponding differences in the underlying patterns of the etchedmicro-features. In some embodiments, the micro-features comprise pillarsor posts, and in other embodiments the micro-features may comprise acombination of a plurality of trenches or holes and a plurality ofpillars or posts.

FIG. 25 shows a schematic block diagram of incident electromagneticradiation (e.g., infrared rays) being focused to three distinct focalpoints by corresponding elements of a 3×1 planar GRIN lens array 84. Theuse of a multi-aperture lens system allows variations in the way theindividual aperture collects information from a scene, includingindependent aspheric and diffractive surface design of different lenseswithin the array 84, off-axis mounting, diversity in field of view,capture time, digital zoom, and even variations in focal plane. Thisinformation enables a processor 60 to perform a wide range ofreconstruction analysis with an image reconstruction program 62, whichin turn may provide more information about a scene than could beavailable from a single aperture system.

The thermal imaging device 14 can be configured to process scene datafrom all available pixels on the FPA/ROIC substrate 20 to achieve thehighest possible resolution, or from a subset of the pixels to reducepower consumption, depending on the user's requirements. The use ofmultiple apertures provides an “oversampling” of the image. Therefore,even if the image from one of the pixels is defective (e.g., due tomis-calibration of the pixels during field operation, defects duringmanufacturing, or failures in the field), the resulting digitallyreconstructed image can compensate for that based on the informationfrom the remaining functional pixels. The processor 60 receives signalsor data from the readout integrated circuit and executes an imagereconstruction program 62 to construct a higher resolution image fromthe multiple low-resolution images from the various lenses in the array84. Examples of suitable image reconstruction programs are those used inmulti-spectral, super-resolution, and/or plenoptic imaging schemes.Computer programs may be stand-alone software entities or sub-entities(e.g., subroutines, code objects) of other computer programs.

FIG. 26 is a block diagram illustrating the imaging of a scene with oneor more GRIN lenses and reconstruction of the original image by digitalreconstruction and/or super-resolution techniques. Each focused spot ofelectromagnetic radiation individually forms an image on a correspondingpixel sub-array in a focal plane array. For example, one may obtain nineindependent images with a 3×3 array of pixels in a focal plane. Thesenine images can be processed to computationally reconstruct a higherresolution image that approaches the original image.

FIG. 27 shows an example of a 3×1 element array 85 of planar GRIN lensesformed in the same lens substrate 86. The three lenses that are formedin the lens substrate 86 are arranged in the same plane with each other.The three lenses have different orientations of their optical axes. Thefirst lens has an optical axis that is offset by an angle θ₁ from a linenormal to the lens substrate 86, the second lens has an optical axisthat is normal to the lens substrate 86, and the third lens has anoptical axis that is offset by an angle θ₂ from a line normal to thelens substrate 86. One possible approach that may be used to tilt theoptical axis of a GRIN lens is to implement a spatial bias within apattern of sub-wavelength micro-features (e.g., trenches or holes) toinduce the variation in the refractive properties of the resulting lens.A configuration in which at least two of the lenses in a lens systemhave different optical axes is useful in some embodiments for providinga desired field of view and/or for directing the incidentelectromagnetic radiation to desired focused spots on the FPA/ROICsubstrate 20.

In some embodiments, a planar GRIN lens may comprise two or more stackedsubstrates that are attached (e.g., bonded) together. Such substratestacking schemes may be implemented to support several objectives, suchas overcoming DRIE aspect ratio limitations and providing mechanicalrobustness. It is understood that references to a lens substratethroughout the present disclosure may refer to either a single substrateor to a stack comprising a plurality of substrates.

FIG. 28 is a block diagram showing an idealized deep reactive ionetching (DRIE) process that may produce micro-features with verticalsidewalls. However, an actual DRIE process is typically characterized bya finite sidewall angle as depicted by the sidewall angle θ in FIG. 29.In some examples, the sidewall angle θ is in the range of 80° to 100°from the plane of the substrate. In some examples, the sidewall angle isstepped (i.e., assumes more than one value over the depth of a feature).In some embodiments, it is advantageous to form planar GRIN lenses withtrenches or holes having a depth in the range of 40 to 200 μm (toachieve desired focusing power) and a width or diameter in the range of0.5 to 4 μm (to satisfy the EMT criterion). Thus, in some embodiments,the depth-to-width aspect ratio for the trenches or holes may be in therange of about of 12:1 to 400:1, and preferably greater than or equal to30:1. However, a typical silicon DRIE process may only readily supportan aspect ratio in the range of 40:1 to 145:1. In some such cases, it ispossible to scale the maximum effective achievable etch aspect ratio byforming a stack of separately etched substrates.

FIG. 30 shows a keyhole-shaped profile of the micro-features, achievedby stacking two etched substrates 88A and 88B. The first substrate 88Ais stacked on the second substrate 88B such that etched trenches orholes 89A in the first substrate are aligned with corresponding trenchesor holes 89B in the second substrate to form combined trenches or holes.Each of the combined trenches or holes preferably has a width ordiameter that is less than a wavelength of incident electromagneticradiation, the spacing between adjacent ones of the combined trenches orholes is less than the wavelength of the electromagnetic radiation, andthe size and spacing of the combined trenches or holes in the stackedsubstrates 88A and 88B are sufficient to produce an effective refractiveindex profile of the lens element that is graded (e.g., varying as afunction of radial position from its center). FIG. 31 shows anotherembodiment of a GRIN lens having combined trenches or holes withdiamond-shaped profiles achieved by stacking two etched substrates 90Aand 90B.

As a specific example of stacking substrates, a DRIE process with 40:1aspect ratio may be used to form a series of trenches or through-holesin two separate silicon (Si) substrates. Each of the substrates has athickness of 80 μm. The trenches or holes have a width or diameter ofabout 2 μm. The two etched substrates are bonded (for example, using afusion bonding process) such that the through-holes or trenches on eachsubstrate are aligned to form combined trenches or holes. The result isstacked substrates having a combined thickness of 160 μm with holes ortrenches having a width of only 2 μm, thereby doubling the effectiveaspect ratio enabled by the DRIE process from 40:1 to 80:1. In someembodiments, the etched Si layer is a device layer of a SOI wafer thatis separated from the carrier wafer as part of the stacking process.

The desire for mechanical robustness may provide another incentive forstacking substrates to form a GRIN lens. A boxed in cross-sectionincreases the bending stiffness of the lens, which may be desirable toresist a pressure differential imparted by a vacuum within a FPA cavity.A second use of an enclosed substrate is to protect fine etchedmicro-features (such as trenches or holes having high aspect ratios)from particulate contaminants, moisture absorption and mechanical damagesustained from contact with foreign objects. In some embodiments, atleast one of the substrates forming the GRIN lens (or at least one lidattached to the substrate) has a substantially flat, planar surfaceenclosing the micro-features an entrance side through which theelectromagnetic radiation enters the lens, and the micro-features areformed in an exit side of the substrate through which theelectromagnetic radiation exits. In some embodiments, the exit side mayalso be enclosed, preferably by a substantially flat, planar surface. Athird benefit of enclosed micro-features in a lens substrate(s) isincreased thermal isolation across the thickness of the substrate byreducing convection heat transfer in the etched trenches or holes. Threepossible approaches for forming enclosed micro-features in substratestacks are illustrated in FIGS. 32, 33 and 34.

In FIG. 32, a DRIE or other suitable process is used to form blind holesor trenches 93 in a silicon substrate 91, thereby leaving a firstenclosed surface 94. A lid substrate 92, formed for example using thedevice layer of a SOI wafer, may be bonded to the DRIE process side ofthe substrate 91 to form a second enclosed surface 95. In FIG. 33, aDRIE or other suitable process is used to form through holes or trenchesin a silicon substrate 96. A first lid substrate 97A, formed for exampleusing the device layer of a SOI wafer, may be bonded to a first side ofthe substrate 96 to form a first enclosed surface. Similarly, a secondlid substrate 97B, also formed for example using the device layer of aSOI wafer, may be bonded to a second side of the substrate 96 to form asecond enclosed surface. In FIG. 34, DRIE or other suitable processesare used to form blind holes or trenches in first and second siliconsubstrates 98A and 98B, respectively, thereby leaving a first enclosedsurface on each substrate. The etched sides of the first and secondsubstrates 98A and 98B are bonded together, for example using a fusionbonding process, thereby forming fully enclosed micro-features (e.g.,trenches or holes).

FIG. 35 shows an embodiment in which diffractive elements 99 are formedon a planar GRIN lens substrate 100 as distinct structures from theetched trenches or holes 101 that are used to impart the refractivebehavior of the lens. The diffractive elements 99 may be formed using athin film or etched into the bulk substrate 100. Furthermore, thediffractive elements 99 may be formed on either or both surfaces of thelens substrate 100. In other embodiments, diffractive elements may beimplemented in several different ways. For example, in some embodiments,diffractive elements are incorporated and arranged with the etchedmicro-features that are used to impart the refractive behavior of thelens on a planar GRIN lens substrate. The diffractive elements may beformed in the lens substrate using, for example, a separate etchprocess. Diffractive optical elements are optional features tocompensate for dispersion and optical aberrations within a planar GRINlens.

FIG. 36 shows another embodiment of a gradient-index lens for focusingincident electromagnetic radiation. The lens comprises at least onesubstrate 102 having first and second opposing sides 104A, 104B (top andbottom sides in the drawing, although the relative orientation may varyduring use). The first side 104A has a first set of trenches or holes106A formed therein (e.g., blind holes or blind trenches that do notextend all the way through the substrate), and the second side 104B hasa second set of trenches or holes 106B formed therein (e.g., blind holesor blind trenches that also do not extend all the way through thesubstrate). The size and spacing of the trenches or holes 106A, 106Bformed in both of the sides of the substrate 102 are sufficient toproduce an effective refractive index profile of the lens that isgraded. In some embodiments, the refractive index profile is aspheric.Forming micro-features 106A, 106B in both sides of the substrate 102 isuseful in embodiments where it is desired to remove more material fromthe substrate (e.g., by etching) to achieve a desired index ofrefraction.

FIGS. 37A-F are schematic diagrams illustrating fabrication steps forproducing the lens of FIG. 36, according to some embodiments of theinvention. In FIG. 37A, the substrate 102 (e.g., a single-crystalsilicon substrate) is ground to a desired thickness (e.g., 100 to 400μm) and polished on first and second sides 104A, 104B. In FIG. 37B,oxide hardmasks 108A, 108B (e.g., layers of silicon dioxide, each havinga thickness in the range of 0.25 to 2 μm) are deposited on the first andsecond sides of the substrate 102. The hardmasks 108A, 108B may bedeposited on both sides of the substrate 102 simultaneously if performedby low-pressure chemical vapor deposition (LPCVD), or one side of thesubstrate 102 at a time if performing plasma-enhanced chemical vapordeposition (PECVD) or physical vapor deposition (PVD). In FIG. 37C, thehardmask 108A is patterned by lithography and etching to a correspondingpattern for the trenches or holes to be etched in the first side of thesubstrate 102. In FIG. 37D, the hardmask 108B is patterned bylithography and etching to a corresponding pattern for the trenches orholes to be etched in the second side of the substrate 102.

In FIG. 37E, the micro-features 106A (e.g., trenches or holes) areformed in the top side of the substrate 102 preferably by deep reactiveion etching. The trenches or holes preferably have a depth in the rangeof 20 to 100 μm and a width or diameter in the range of 0.5 to 4 μm. InFIG. 37F, the micro-features 106B (e.g., trenches or holes) are formedin the second side of the substrate 102 by deep reactive ion etching(e.g., to a depth in the range of 20 to 100 μm). The hardmasks 108A,108B are removed (e.g., using HF vapor) to result in the structure ofthe substrate 102 shown in FIG. 36. Many other fabrication techniquesare possible in alternative embodiments. For example, in someembodiments it is helpful to use one or more handle wafers if thesubstrate 102 is too thin after grinding and/or delicate after the firstDRIE step. A handle or carrier wafer may be bonded to the substrate 102to provide support or ease of handling, and then later removed.

FIG. 38 is a schematic side view of another GRIN lens, according to someembodiments of the invention. The lens includes the substrate 102(described above with micro-features formed in both sides) and a secondsubstrate 110 having at least one side with another set of trenches orholes formed therein. The substrates 102, 110 are attached to each other(e.g., bonded) such that the trenches or holes in the substrate 110 aresubstantially aligned with trenches or holes in the substrate 102 toform combined trenches or holes 107 that are fully enclosed. Thesubstrate 110 optionally includes micro-features etched into its firstand second sides, similar to the substrate 102. In this case, anoptically transmissive lid 112 (e.g., a substrate) is useful. One sideof the stack of substrates 102, 110 that may be exposed to thesurrounding environment during use of the lens is capped with a siliconlid 112 to keep out contaminants and protect the micro-features.Alternatively, both sides of the stack of substrates 102, 110 may becapped with lids. In some embodiments, the second substrate 110 may onlyhave blind holes or trenches etched in one side that is attached to thefirst substrate 102, in which case a lid may not be necessary.Diffractive elements may be etched in the second substrate 110, similarto the diffractive elements shown in FIG. 30.

The description above illustrates embodiments of the invention by way ofexample and not necessarily by way of limitation. Many other values maybe selected for the specific depths, trench or hole sizes, and indexcoefficients, as well as different combinations of parameters and/ormaterials. The GRIN lenses may be incorporated into a camera having anoptically transmissive lid (e.g., formed using germanium or silicon)that is provided as part of the overall vacuum package and that servesas a window for incident IR radiation. The infrared (IR) cameratypically includes a camera core comprising a Focal Plane Array (FPA), alens system and an enclosure. The FPA typically comprises multipleelements—the underlying Read-Out Integrated Circuit (ROIC), thethermistor or micro-bolometer pixel array which is built on top of theROIC, usually on the same silicon wafer and integrated with the ROIC,and a “packaged window” or lid (e.g., formed using germanium or silicon)which is substantially transparent to incoming IR radiation and which isbonded on top of the FPA with a hermetic vacuum seal. A single GRIN lensor a system of GRIN lenses is mounted on top of the FPA (e.g., one ormore GRIN lenses may be screwed on or molded to a housing).

In some embodiments, one or more GRIN lenses formed in at least onesubstrate may form the vacuum package with the FPA, eliminating the needfor a separate “packaged window” or lid. In some embodiments, refractiveoptical elements may be provided, such as an etched refractive surfaceformed in one or more lens substrates. Imaging devices (e.g., cameracores) may include just one lens substrate and one pixel, or the imagingdevices may comprise multiple lenses, lens substrates and/or pixelarrays. The imaging devices may be used in a wide range of applicationssuch as expanded security, surveillance, first responder, and automotiveapplications.

The planar GRIN lens substrate may further comprise a series of lenscarriers, wherein each lens carrier comprises a “shelf” or “ledge”structure to align and support a corresponding discrete lens, and athrough “window” to pass incident electromagnetic radiation. A discretelens may be positioned onto a corresponding lens carrier using, forexample, a pick and place process. In some configurations, a discretelens is attached to the lens carrier using a hermetic bond formed using,for example, a fusion bonding, brazing, or solder process.Multi-spectral imaging schemes may thus be implemented by pairingindividual lenses on a lens substrate to corresponding detectors on aFPA substrate. As an example, a lens substrate may be formed having amonolithic planar GRIN lens disposed over a micro-bolometer-based FPA tosupport infrared imaging and a discrete lenticular glass lens assembledin a lens carrier disposed over a CMOS-based FPA to support visiblelight imaging. This modular approach to multi-spectral imaging may bereadily extended to additional bands of electromagnetic radiationincluding, for example, near-infrared (NIR) and ultraviolet (UV), usingsuitable pairs of lenses and detectors.

Accordingly, the scope of the invention should be determined by thefollowing claims and their legal equivalents.

What is claimed is:
 1. A gradient-index lens for directing incidentelectromagnetic radiation within a wavelength range of about 8 to 15 μm,the lens comprising at least one germanium or silicon substrate having aplurality of trenches formed therein, wherein each of the trenches hasat least one dimension that is less than 8 μm, each of the trenches hasa ratio of length to width that is greater than or equal to 3:1, amajority of the trenches have an aspect ratio of depth to width greaterthan or equal to 30:1, the spacing between adjacent trenches is lessthan 8 μm, and an effective refractive index profile of the lens isgraded.
 2. The lens of claim 1, wherein each of the trenches has across-sectional area in a plane substantially perpendicular to a linedefining the depth of the trench, and the cross-sectional area issubstantially shaped like an arc, spiral, circle or ring.
 3. The lens ofclaim 1, wherein the trenches are shaped like arcs that are arranged ina pattern of substantially concentric circles or rings havingdiscontinuities that are less than 8 μm.
 4. A camera comprising at leastone pixel in a focal plane, wherein the lens of claim 1 is arranged todirect the electromagnetic radiation to the pixel.
 5. The camera ofclaim 4, further comprising at least one readout circuit electricallyconnected to the pixel, and further comprising at least one processor incommunication with the circuit, wherein the processor is programmed toconstruct an image from pixel signals.
 6. The lens of claim 1, whereineach of the trenches has at least one dimension that is in the range of150 nm to 2 μm, and the spacing between adjacent trenches is the rangeof 150 nm to 2 μm.
 7. The lens of claim 1, wherein the lens has asubstantially flat surface enclosing the trenches on an entrance sidethrough which the electromagnetic radiation enters the lens, and whereinthe trenches are formed in an exit side of the substrate through whichat least a portion of the electromagnetic radiation exits.
 8. The lensof claim 1, further comprising diffractive elements formed in thesubstrate.
 9. The lens of claim 1, wherein each of the trenches has adepth in the range of 40 to 200 μm and a width in the range of 0.5 to 4μm.
 10. The lens of claim 1, wherein the majority of the trenches havean aspect ratio of depth to width greater than or equal to 80:1.
 11. Thelens of claim 1, wherein the substrate has first and second opposingsides, a first set of the trenches is formed in the first side, and asecond set of the trenches is formed in the second side.
 12. Agradient-index lens for directing incident electromagnetic radiationwithin a wavelength range of about 8 to 15 μm, the lens comprising atleast one germanium or silicon substrate having a plurality of trenchesor holes formed therein, wherein each of the trenches or holes has atleast one dimension that is less than 8 μm, the spacing between adjacenttrenches or holes is less than 8 μm, an effective refractive indexprofile of the lens is graded, and the f-number divided by the diameterof the lens is less than 1.5/mm.
 13. The lens of claim 12, wherein eachof the trenches or holes has at least one dimension that is in the rangeof 150 nm to 2 μm, and the spacing between adjacent trenches or holes isthe range of 150 nm to 2 μm.
 14. The lens of claim 12, wherein thef-number divided by the diameter of the lens is in the range of 0.05 to1.5/mm.
 15. The lens of claim 12, wherein each of the trenches or holeshas a depth in the range of 40 to 200 μm and a width or diameter in therange of 0.5 to 4 μm.
 16. The lens of claim 12, wherein a majority ofthe trenches or holes have an aspect ratio of depth to width greaterthan or equal to 30:1.
 17. The lens of claim 12, wherein the substratehas first and second opposing sides, a first set of the trenches orholes is formed in the first side, and a second set of the trenches orholes is formed in the second side.
 18. The lens of claim 12, furthercomprising diffractive elements formed in the at least one substrate.19. A camera comprising at least one pixel in a focal plane, wherein thelens of claim 12 is arranged to direct the electromagnetic radiation tothe pixel.
 20. The camera of claim 19, further comprising at least onereadout circuit electrically connected to the pixel, and furthercomprising at least one processor in communication with the circuit,wherein the processor is programmed to construct an image from pixelsignals.